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Numerical study of Lorenz’s equation by the Adomian method. (English) Zbl 0869.65044
Summary: We use the decomposition method of Adomian for solving differential systems coming from physics (meteorology). We also give a comparison between the Runge-Kutta method and the decomposition technique. Furthermore, we reconfirm the famous “butterfly effect”.

65L05Initial value problems for ODE (numerical methods)
65L60Finite elements, Rayleigh-Ritz, Galerkin and collocation methods for ODE
34A34Nonlinear ODE and systems, general
86A10Meteorology and atmospheric physics
Full Text: DOI
[1] Adomian, G.: Nonlinear stochastic systems and application to physics. (1989) · Zbl 0659.93003
[2] Adomian, G.: A review of the decomposition method and some results for nonlinear equations. Mathl. comput. Modelling 13, No. 7, 17-43 (1990) · Zbl 0713.65051
[3] Adomian, G.: Solving frontier problems of physics: the decomposition method. (1994) · Zbl 0802.65122
[4] Abbaoui, K.; Cherruault, Y.: Convergence of Adomian’s method applied to differential equations. Mathl. comput. Modelling 28, No. 5, 103-109 (1994) · Zbl 0809.65073
[5] Abbaoui, K.; Cherruault, Y.: New ideas for proving convergence of decomposition methods. Computers math. Applic. 29, No. 7, 103-108 (1995) · Zbl 0832.47051
[6] Cherruault, Y.: Convergence of Adomian’s method. Kybernetes 18, No. 2, 31-38 (1989) · Zbl 0697.65051
[7] Cherruault, Y.; Adomian, G.: Decomposition method: A new proof of convergence. Mathl. comput. Modelling 18, No. 12, 103-106 (1993) · Zbl 0805.65057
[8] Cherruault, Y.; Adomian, G.; Abbaoui, K.; Rach, R.: Further remarks on convergence of decomposition. I.j.b.c. 38, 89-93 (1995)
[9] Guellal, S.; Cherruault, Y.: Practical formulae for calculation of Adomian’s polynomials and application to the convergence of the decomposition method. I.j.b.c. 36, 223-228 (1994)
[10] Abbaoui, K.; Cherruault, Y.; Seng, V.: Practical formulae for the calculus of multivariable Adomian’s polynomials. Mathl. comput. Modelling 22, No. 1, 89-93 (1995) · Zbl 0830.65010
[11] Abbaoui, K.; Cherruault, Y.; N’dour, M.: The decomposition method applied to differential equation systems. Kybernetes 24, No. 8, 32-40 (1995) · Zbl 0932.65081
[12] Sparrow, C.: The Lorenz equations: bifurcations, chaos and stranger attractors. (1985)
[13] P. Grimalt, Hacia modelaciones matemáticas del músculo cardiaco: Bases y teorías que lo fundamentan, Fundación general de la Universidad Complutense de Madrid, Cursos de verano del Escorial, Madrid (to appear).
[14] Kaplan, D.; Glass, L.: Understanding non-linear dynamics. (1995) · Zbl 0823.34002
[15] Guellal, S.; Cherruault, Y.: Application of the decomposition method to identify the distributed parameters of elliptical equation. Mathl. comput. Modelling 21, No. 4, 51-55 (1994) · Zbl 0822.65120